This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Sample Midterm 2, Math 33A, Fall 2007 November 19, 2007 1. (2 pts each) Indicate whether each statement is true or false; you need not show your work here. If T : R n → R n is an invertible linear transformation, B is a basis of R n , and B is the matrix of T with respect to the basis B , then B must be invertible. T F If A is a n by n matrix with exactly one 1 in each row, exactly one 1 in each column, and 0s elsewhere, then det A must be 1 or 1. T F If A is a n by n matrix, then det 2 A must be equal to 2(det A ). T F If ~v is a vector in R n and W is a subspace of R n , then the length of proj W ~v must be less than or equal to the length of ~v . T F . If W and V are subspaces of R n and W ⊂ V , then it must also be true that W ⊥ ⊂ V ⊥ . T F . Solution. T, T, F, T, F. If T : R n → R n is an invertible linear transformation and A is its matrix with respect to the standard basis, then A is invertible. If S is the changeofbasis matrix for the basis B , then B = S 1 AS , which is a product of invertible matrices. Hence, which is a product of invertible matrices....
View
Full
Document
This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
 Fall '08
 lee
 Math

Click to edit the document details